For pockets, I like PUL outers and suedecloth inners: microfleece inners feel better to me, but it is a PITA to sew with.

For fitteds, I really like flannel. I don't really care for knits. I feel like, if I wanted to sew with difficult to handle materials, I'd be sewing a pocket, If I want a stay-dry inner to the fitted, I'd use suedecloth.

I stuff pockets with prefolds or flats, usually. For a fitted, the soaker might involve flannel, terry, and microfiber in various combinations.

For fitteds I love cotton fleece and bamboo-cotton fleece for absorbent inners, cute cotton knits for outers, and cotton velour for inners. All of my covers are pull on style fleece soakers/shorties/longies.

Right now I am making a ton of newborn fitteds and I am loving the knit outers and cotton velour inners--so soft and squishy! For waterproof pockets, I use pul and usually an inner of suedecloth or microfleece. I also love using recycled wool sweaters to make soakers/longies and shorties.